A.R. Forsyth Calculus of Variations Dover Publications Inc. 1960
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July 26, 2013
An Amazing Book
Forsyth's Calculus of Variations was published in 1927, and is a marvelous example of solid early twentieth century mathematics. It looks at how to find a FUNCTION that will minimize a given integral. The book looks at half-a-dozen different types of problems (dealing with different numbers of independent and dependent variables). It looks at weak and strong variations. This book covers several times more material than many modern books on Calculus of Variations. The down-side, of course, is that the proofs move quickly (it can take the reader a few hours to fill in the missing steps in order to verify Forsyth's calculations in a proof) and do not worry about truely bizarre behavior (such as encountered in nonlinear dynamics). But the proofs are complete (given the 1927 understanding of derivatives of functions) and quite solid (again, by 1927 standards).
I reccomend this book to anyone who wishes to explore the wild, wild world of Calculus of Variations. Yes, there are easier books on the subject, but this one is a gem.